In the past few years it is observed renewed interest in the study of non-relativistic string theories in Newton-Cartan (NC) formulation
[1]}, [2]}. Basically, NC gravity provides
covariant description of Newton's law. However it is very remarkable
that NC description can be extended also into more broader class of theories,
as for example field theory and string theory. In fact, non-relativistic string theory
was originally introduced in 2000 in two papers
[3]}, [4]}. These theories were defined without
Newton-Cartan formalism which was firstly introduced in the context of string theory in the
remarkable paper [5]}, for related works, see
for example
[6]}, [7]}, [8]}, [9]}, [10]}, [11]}, [12]}, [13]}, [14]}, [15]}, [16]}, [17]}, [18]}, [19]}, [20]}, [21]}, [22]}. Different formulation of non-relativistic string
was presented in
[23]} that was based on T-duality of string theory
in the background with null isometry
For related works, see
[24]}, [25]}, [26]}, [27]}, [28]}, [29]}, [30]}, [31]}, [32]}, [33]}, [34]}, [15]}.. In [6]} new form of non-relativistic
string theory was proposed that has interesting property that non-relativistic string
naturally couples to two form field \(m_{MN}\)  in the similar way as non-relativistic particle couples to mass form \(m_M\) .
